1 A revisit of parametrization of downward longwave radiation in
2 summer over the Tibetan Plateau based on high temporal resolution
3 measurements
4 Mengqi Liua,c, Xiangdong Zhengd, Jinqiang Zhanga,b,c and Xiangao Xiaa,b,c
5 a LAGEO, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing,
6 100029, China
7 b Collaborative Innovation Center on Forecast and Evaluation of Meteorological
8 Disasters, Nanjing University of Information Science & Technology, Nanjing 210044,
9 China
10 c College of Earth and Planetary Sciences, University of Chinese Academy of Sciences,
11 Beijing, 100049, China
12 d Chinese Academy of Meteorological Sciences, Chinese Meteorological Bureau,
13 Beijing, 100081, China
14 15
1
16 Abstract 17 The Tibetan Plateau (TP) is one of research hot spots in the climate change research
18 due to its unique geographical location and high altitude. Downward longwave
19 radiation (DLR), as a key component in the surface energy budget, is of practical
20 implications for radiation budget and climate change. A couple of attempts have been
21 made to parametrize DLR over the TP based on hourly or daily measurements and crude
22 clear sky discrimination methods. This study uses 1-minute shortwave and longwave
23 radiation measurements at three stations over TP to parameterize DLR during summer
24 months. Three independent methods are used to discriminate clear sky from clouds
25 based on 1-minute radiation and Lidar measurements. This guarantees strict selection
26 of clear sky samples that is fundamental for the parameterization of clear-sky DLR.
27 Eleven clear-sky and four cloudy DLR parameterizations are examined and locally
28 calibrated. Comparing to previous studies, DLR parameterizations here are shown be
29 characterized by smaller root mean square error (RMSE) and higher coefficient of
30 determination (R2). Clear-sky DLR can be estimated from the best parametrization with
31 RMSE of 3.8 W⸱m-2 and R2 > 0.98. Systematic overestimation of clear-sky DLR by the
32 locally calibrated parametrization in one previous study is found to be approximately
33 25 W⸱m-2 (10%), which is very likely due to potential residual cloud contamination on
34 previous clear-sky DLR parametrization. Cloud-base height under overcast conditions
35 is shown to play an important role in cloudy DLR parameterization, which is considered
36 in the locally calibrated parameterization over the TP for the first time. Further studies
37 on DLR parameterization during nighttime and in seasons except summer are required
38 for our better understanding of the role of DLR in climate change.
39 40
2
41 1 Introduction
42 The downward longwave radiation (DLR) at the Earth’s surface is the largest
43 component of the surface energy budget, being nearly double the downward shortwave
44 radiation (DSR) (Kiehl and Trenberth, 1997). DLR has shown a remarkable increase
45 during the process of global warming (Stephens et al., 2012). This is closely related to
46 the fact that both a warming and moistening of the atmosphere (especially at the lower
47 atmosphere associated with the water vapor feedback) positively contribute to this
48 change. Understanding of complex spatiotemporal variation of DLR and its implication
49 is necessary for improving weather prediction, climate simulation as well as water
50 cycling modeling. Unfortunately, errors in DLR are considered substantially larger than
51 errors in any of the other components of surface energy balance, which is most likely
52 related to the lack of DLR measurements with high quality (Stephens et al., 2012).
53 The 2-sigma uncertainty of DLR measurement by using a well-calibrated and
54 maintained pyrgeometer is estimated to be 2.5% or 4 W⸱m-2 (Stoffel, 2005). However,
55 global-wide surface observations are very limited, especially in some remote regions.
56 On the other hand, it has been known for almost one century that clear-sky DLR is
57 determined by the bulk emissivity and effective temperature of the overlying
58 atmosphere (Ångström, 1918). Since these two quantities are not easily observed for a
59 vertical column of the atmosphere, clear-sky DLR is widely parameterized as a function
60 of surface air temperature and water vapor density, assuming that the clear sky radiates
61 toward the surface like a grey body at screen-level temperature. Dozens of
62 parameterization formulas of DLR have been developed in which clear-sky effective
63 emissivity (εc) is a function of the screen-level temperature (T) and water vapor pressure
64 (e) (T and e have the same meaning and unit in following equations if not specified), or
65 simply in the localized coefficients with given functions. Two formulas, i.e., an
66 exponential function (Idso, 1981) and a power law function (Brunt, 1932; Swinbank,
67 1963), have been widely used to depict the relationship of εc to T and e. The coefficients
68 of these functions are derived by a regression analysis of collocated measurements of
69 T, e and DLR. Most of these proposed parameterizations are empirical in nature and
70 only specific for definite atmospheric condition. An exception is that Brutsaert (1975) 3
71 developed a model based on the analytic solution of the Schwarzchild’s equation for a
72 standard atmospheric lapse rates of T and e. Prata (1996) found that the precipitable
73 water content (w) was much better to represent the effective emissivity of the
74 atmosphere than e, which was loosely based on radiative transfer simulations. Dilley
75 and O’Brien (1998) adopted this scheme but tuned empirically their parameterization
76 using an accurate radiative transfer model. Since DLR is to some extent impacted by
77 water vapor and temperature profile (especially in case of existence of an inversion
78 layer) and diurnal variation of T, a new model with two more coefficients considering
79 these effects was developed (Dupont et al., 2008).
80 In the presence of clouds, total effective emissivity of the sky is remarkably
81 modulated by clouds. The existing clear-sky parameterization should be modified
82 according to the cloud fraction (CF) and other cloud parameters such as cloud base
83 height (CBH). CF is generally used to represent a fairly simple cloud modification
84 under cloudy conditions. Dozens of equations with cloudiness correction have been
85 developed and evaluated by DLR measurements across the world (Crawford and
86 Duchon, 1999; Niemelä et al., 2001). CF can be obtained by trained human observers
87 (Iziomon et al., 2003) or derived from DSR (Crawford and Duchon, 1999) and DLR
88 measurements (Dürr and Philipona, 2004). High temporal resolution of DSR or DLR
89 measurements (for example, 1-minute) can also provide cloud type information
90 (Duchon and O’Malley, 1999), and thereby allow to consider potential effects of cloud
91 types on DLR (Orsini et al., 2002).
92 With an average altitude exceeding 4 km above the sea level (ASL), the Tibetan
93 Plateau (TP) exerts a huge influence on regional and global climate through mechanical
94 and thermal forcing because of its highest and most extensive highland in the world
95 (Duan and Wu, 2006). TP, compared to other high altitude regions and the poles, has
96 been relatively more sensitive to climate change. The most rapid warming rate over the
97 TP occurred in the latter half of the 20th century likely associated with relatively large
98 increase in DLR. Duan and Wu (2006) indicated that increase in low level nocturnal
99 cloud amount and thereby DLR could partly explain the increase in the minimum
100 temperature, despite decrease in total cloud amount during the same period. By using 4
101 observed sensitivity of DLR to change in specific humidity for the Alps, Rangwala et
102 al. (2009) suggested that increase in water vapor appeared to be partly responsible for
103 the large warming over the TP. Since the coefficients of certain empirical
104 parameterizations and their performances showed spatiotemporal variations,
105 establishment of localized DLR parameterizations over the TP is of high significance.
106 Further studies on DLR, including its spatiotemporal variability, its parameterization as
107 well as its sensitivity to changes in atmospheric variables, would be expected to
108 improve our understanding of climate change over the TP (Wang and Dickinson, 2013).
109 DLR measurements from high quality radiometer with high temporal resolution
110 over the TP are quite scarce. To the best of our knowledge, there are very few
111 publications on DLR and its parameterization over the TP. Wang and Liang (2009)
112 evaluated clear-sky DLR parameterizations of Brunt (1932) and Brutsaert (1975) at 36
113 globally distributed sites, in which DLR data at two TP stations were used. Yang et al.
114 (2012) used hourly DLR data at 6 stations to study major characteristics of DLR and to
115 assess the all-sky parameterization of Crawford and Duchon (1999). Zhu et al. (2017)
116 evaluated 13 clear-sky and 10 all-sky DLR models based on hourly DLR measurements
117 at 5 automatic meteorological stations. The Kipp & Zonen CNR1 is composed of CM3
118 pyranometer and CG3 pyrgeometer that are used to measure DLR and DSR,
119 respectively. The CG3 is the second class radiometer according to the International
120 Organization for Standardization (ISO) classification. The root mean square error of
121 hourly DLR is less than 5 W⸱m-2 after field recalibration and window heating correction
122 (Michel et al., 2008). Note that human observations of cloud every 3-6 hours or hourly
123 DLR and DSR data are respectively used to determine clear sky and cloud cover in
124 these previous studies.
125 In order to further our understanding of DLR and DSR over the TP, measurements
126 of 1-minute DSR and DLR at 3 stations over the TP using state-of-the-art instruments
127 have been performed in summer months since 2011. These data provide us opportunity
128 to evaluate clear-sky DLR models and quantitatively assess cloud impacts on DLR.
129 This study makes progress in the following aspects as compared to previous studies: 1)
130 clear-sky discrimination and CF estimation are based on 1-minute DSR and DLR 5
131 measurements that are objective in nature; 2) misclassification of cloudiness into cloud-
132 free skies would be minimized by adopting strict cloud-screening procedures based on
133 1-minute DSR, DLR and Lidar measurements; 3) potential effects of CBH on DLR are
134 also investigated. Localized parameterizations of clear-sky and all-sky DLRs are finally
135 achieved, which would be expected to improve DLR estimations over the TP.
136
137 2. Site, Instrument and Data
138 Measurements of DLR and DSR conducted 1~4 months over the TP at three
139 stations (Table 1), including Nagqu (NQ, 92.04°E, 31.29°N, 4507 m ASL), Nyingchi
140 (NC, 94.2°E, 29.4°N, 2290 m ASL) and Ali (AL, 80°E, 32.5°N, 4287 m ASL) are used
141 for the DLR parameterization. DLR and DSR were respectively measured by CG4 and
142 CM21 radiometers (Kipp & Zonen, Delft, Netherlands). The sampling frequency is 1
143 Hz and the averages of the samples over 1-minute intervals are logged on a Campbell
144 Scientific CR23X datalogger. Simultaneous 1-minute averages of T and e are taken
145 from the automatic meteorological stations. With the aid of its specific material and
146 unique construction, CG4 is designed for the DLR measurement with high reliability
147 and accuracy. Window heating due to absorption of solar radiation in the window
148 material, the major error source of DLR measurement, is strongly suppressed by its
149 unique construction conducting away the absorbed heat very effectively. CM21 is a
150 high performance research grade pyranometer. Introduction of individually optimized
151 temperature compensation for CM21 makes it have much a smaller thermal offset than
152 CM3. The installation of the CG4 and CM21 on the Kipp & Zonen CV2 ventilation
153 unit prevents dew deposition on the window of the CG4 and the quartz dome of the
154 CM21. The radiometers are calibrated before and after field measurements to the
155 standards held by the China National Centre for Meteorological Metrology.
156 A Micropulse Lidar (MPL-4B, Sigma Space Corporation, United States) was
157 installed side-by-side with radiometers. The Nd:YLF laser of the MPL produces an
158 output power of 12 μJ at 532 nm. The repletion rate is 2500 Hz. The vertical resolution
159 of the MPL data is 30 m and the integration time of the measurements is 30s. The MPL
160 backscattering profiles are used to identify the cloud boundaries and derive the CBHs 6
161 (He et al., 2013). The dataset used in this article contains about 700 hours of coincident
162 DLR, DSR, Lidar and meteorological measurements.
163 DLR and DSR were also measured at Lhasa (91.1°E, 29.9°N, 3649 m ASL) during
164 summer in 2012 using the same instruments as those in other stations. Lhasa data are
165 mainly used for independent validation because of no Lidar data there.
166
167 3. Methods
168 3.1 Clear-sky discrimination
169 Clear skies should be discriminated from cloudy conditions before performing
170 DLR parametrization, which is achieved by the synthetical analysis of DSR, DLR, and
171 CBH from MPL.
172 Following the method initiated by Crawford and Duchon (1999), we calculate two
173 quantities reflecting DSR magnitude and variability based on 1-minute observed DSR
174 (DSRobs) and calculated clear-sky DSR (DSRcal) values. DSRcal is calculated by the
175 model C of Iqbal (1983), in which direct and diffuse DSR are parametrized separately.
176 Direct DSR (DSRdir) is calculated as follows.
177 퐷푆푅푑푖푟 = 푆0휏푟휏푊휏표휏푎휏푔 (1)
178 where 휏푟 , 휏푤 , 휏표, 휏푎 and 휏푔 are transmittances due to Rayleigh scattering, water
179 vapor absorption, ozone absorption, aerosol extinction and absorption by uniformly
180 mixed gases O2 and CO2, respectively. Diffuse radiation is estimated as the sum of
181 Rayleigh and aerosol scattering as well as multiple reflectance. Total ozone column
182 (DU) is provided by Brewer spectrophotometer. w values (cm) are from Vaisala-92
183 radiosonde profiles in AL and Global Position System measurements in NC and NQ,
184 respectively. They are used to create linear regression relationship to collocated ground
185 level e (hPa) measurements, which is then used to estimate w from 1-minute
186 measurements of e. Ångström wavelength exponent and Ångström turbidity are from
187 CE-318 sunphotometer observations in NC and AL, while in NQ we adopt the same
188 value as that in AL because their altitudes are similar. Climatic value of single scattering
189 albedo retrieved from long-period CE-318 observation in Lhasa is 0.90 (Che et al.,
190 2019), which is used in three stations. This is reasonable because of high altitude and
7
191 extremely low aerosol loading in TP. Surface Albedo is 0.25 and 0.22 in Al and NQ
192 according to in situ measurements (Liang et al., 2012). In NC, it is 0.183 (Zhao et al.,
193 2011).
-2 194 DSRcal values are first scaled to a constant value of 1400 W⸱m for each minute of
195 each day. We adopt this value according to Duchon and O’Malley (1998) and Long and
196 Ackerman (2000), which only favors for a clear presentation of the normalized and
197 observed DSR values in the same figure. Afterwards, DSRobs values are scaled by
198 multiplying the same set of scale factors. Finally, the mean and standard deviation of
199 the scaled DSR in a 21-minute moving window (±10 minute centered on the time of
200 interest) are used for cloud screening. Selection of the width of 21-minute is empirical
201 but a consequence of having a reasonable time span for estimating the mean and
202 variance (Duchon and O’Malley, 1999). Clear-sky DSR should satisfy three
203 requirements: 1) ratio of DSRobs to DSRcal is within 0.95 to 1.05; 2) difference between
-2 204 scaled DSRobs and DSRcal is less than 20 W⸱m ; and 3) standard deviation (δ) of scaled
-2 205 DSRobs in a 21-minute moving window is less than 20 W⸱m .
206 Temporal variability of DLR is also used for cloud screening according to Marty
207 and Philipona (2000) and Sutter et al. (2004). Here, δ of scaled DLR (scaled to 500
208 W⸱m-2) in a 21-minute moving window is used for this purpose. Cloud-free sample is
209 determined if δ is less than 5 W⸱m-2.
210 Since both DSR and DLR experience difficulties in detecting clouds in the portion
211 of the sky far away from the sun (Duchon and O’Malley, 1999) or high-altitude cirrus
212 clouds (Dupont et al., 2008), coincident MPL backscatter measurements are used to
213 strictly select clear-sky samples. There should be a cloud element somewhere in the sky
214 when MPL identifies cloud, it is thus required that no clouds are detected by MPL in a
215 21-minute moving window, otherwise it is defined as cloudy.
216 Given the fact that these methods are complementary to each other to some extent
217 (Orsini et al., 2002), we use the following strategy to guarantee a proper selection of
218 clear-sky samples. If DSR, DLR and MPL measurements at the time of interest
219 synchronously satisfy these specified clear-sky conditions, the sample is thought to be
220 taken under unambiguously cloud-free condition; on the contrary, the measurement are 8
221 made under unambiguously cloudy condition if any method suggests cloudy. Our
222 following clear-sky and cloudy DLR parameterizations are respectively based on
223 measurements under unambiguously cloud-free (8195 minutes) and cloudy conditions
224 (69318 minutes).
225 Fig. 1 shows an example of clear sky discrimination results based on our method.
226 DSRobs presents a smooth temporal variation from sunrise to about 14:00 (LST), being
227 consistent with DSRclr. Similarly, DLR also varies very smoothly during the same
228 period when 21-minute standard deviations of DLR are < 5 W⸱m-2. Both facts suggest
229 sunny and cloudless skies. This inference is supported by MPL that suggests no cloud
230 detected overhead. Contrarily, abrupt changes of 1-minute DSRobs and DLR are
231 evident during 14:00~17:00 LST and we can see DSRobs occasionally exceeds the
232 expected DSRclr, indicating frequent occurrence of fair weather cumuli clouds. MPL
233 detect a persistent thin cloud layer at 4 km above ground, which agrees with DSR and
234 DLR measurements very well.
235
236 3.2 Cloud fraction estimation
237 Given synoptic cloud observations are very limited and temporally sparse, various
238 parameterizations using DSR or DLR data have been developed to estimate CF (e.g.,
239 Deardorff, 1978; Marty and Philipona, 2000; Dürr and Philipona, 2004; Long et al.,
240 2006; Long and Turner, 2008). Because of good agreement between clear-sky DSRobs
241 and DSRcal calculated by the Iqbal C calculations (Iqbal, 1983; Gubler et al., 2012),
242 with mean bias of 1.7 W⸱m-2 and root mean square error (RMSE) of 10.7 W⸱m-2 (not
243 shown), we use Deardorff (1978)’s method to calculate CF from DSRobs and DSRcal.
244 The method is based on a fairly simple cloud modification to DSR as follows.
DSR 245 CF = 1 − 표푏푠 (2) DSR푐푎푙
246 CF (no unit) has values ranging from 0 to 1. To avoid the error caused by abrupt
247 DSR variation, 21-minute mean DSR value rather than its instantaneous measurements
248 are used here.
249
9
250 4 Results
251 4.1 Clear-sky DLR parameterization evaluation and localization
252 Eleven clear-sky DLR (DLRclr) parameterizations (Table 2) are evaluated based
253 on 1-minute DLR measurements under unambiguously cloud-free conditions. To
254 compare the performance of these 11 models, RMSE and the coefficient of
255 determination (R2) are shown by a Taylor diagram in Fig. 2(a). Relatively smaller
256 RMSE (generally < 15 W⸱m-2) and larger R2 (>0.95) are derived for the Brutsaert (1975);
257 Konzelmann (1994), Dilley and O’Brien (1998) and Prata (1996) models. This is likely
258 because these parameterizations were developed in cool and dry areas, for example, in
259 England (Brutsaert, 1975); in Greenland (Konzelmann, 1994) and dry desert region in
260 Australia (Prata, 1996). The climate in those areas is likely similar to that over the TP
261 to some extent, so those parameterizations are expected to perform well. The higher
262 RMSE (>37 W⸱m-2) and the lower R2 (~0.7) are derived for Swinbank (1963) and Idso
263 and Jackson (1969) models. This can be partly explained by the fact that only T is used
264 in these two methods. Previous studies suggest substantial uncertainty (RMSE >37.5
-2 2 265 W⸱m and R <0.75) if water vapor effect on DLRclr is not accounted for (Duarte et al.,
266 2006). Since w is very low over the TP and thereby DLR is highly sensitive to variation
267 of w in that case, much more attention should be paid to water vapor effect on the
268 parameterization of DLRclr.
269 The coefficients in eleven parameterizations (Table 2) were originally calibrated
270 and determined in different geographical locations; therefore, they may not be the
271 optimal values for the TP. Thus we take use of 1-minute clear-sky DLR samples to
272 locally calibrate the parameters of these parametrizations. We use 10-fold cross-
273 validation method to determine the parameters. This is a widely used method to
274 estimate the skill of a regression model on unseen data. It is expected to result in a less
275 biased or less optimistic estimate of the model skill than other methods, such as a simple
276 train/test split (James et al., 2013). All the data was randomly dividing into 10 groups
277 of approximately equal size, the coefficients are computed by using 9 groups as training
278 set, and the remaining 1 group is used as validation. This procedure is repeated 10 times
279 to get the representational value of coefficients (with the lowest test error). 10
280 The coefficient values derived from the non-linear least-squares fitting of the
281 DLRclr parameterizations (Table 2) over the TP are presented in Table 3. For each fitted
282 parameterization, we calculated RMSE and R2 and the results are shown in Fig. 2b.
283 When using the parameterizations with the locally fitted parameters, the accuracy of
284 the parameterization relative to the published values is obviously improved. Most
285 RMSEs are < 10 W⸱m-2 except the parameterization proposed by Swinbank (1963) and
286 Idso and Jackson (1969) that still produce the worst results (with R2 of 0.71 and RMSE
287 of 15 W⸱m-2) even after the parameters are locally calibrated. This is probably because
288 e is not considered in these two methods.
289 The Dilley and O’Brien (1998)’s parameterization, which is initially developed by
290 considering the adaptation of climatological diversities, is expected to be able to fit the
291 measurements in tropical, mid-latitude and Polar Regions. This expectation is verified
292 by its wide deployment in DLRclr estimations in different climate regimes and altitude
293 levels, for example, in the tropical lowland (eastern Pará state, Brazil) and the mild
294 mountain area (Boulder, the United States) (Marthews et al., 2012; Li et al., 2017).
295 The present study confirms that Dilley and O’Brien (1998) is the best clear-sky
296 parameterization over the TP. The locally calibrated equation is as follows.
푒 푇 6 46.50× 1 297 DLR =−2.53 + 158.10 × ( ) + 106.40 × ( 푇)2 (3) 푐푙푟 273.16 2.50
298 The RMSE and R2 of Eq.(3) are ~3.8 W⸱m-2 and > 0.98 respectively, which are
299 substantially lower than those in previous studies over the TP, for example, the RMSE
300 was 9.5 W⸱m-2 (Zhu et al., 2017). The Dilley and O’Brien (1998)’s parameterization
301 was suggested to be the most reliable estimates of DLRclr over the TP (Zhu et al., 2017).
302 Note that the parameters here differ quite a lot from their values (Zhu et al., 2017), as
303 shown in Eq. (4).
푒 푇 6 46.50× 1 304 DLR =30.00 + 157.00 × ( ) + 97.93 × ( 푇)2 (4) 푐푙푟 273.16 2.50
305 Fig.3 compares instantaneous clear-sky DLR data from measurements against
306 calculations by Eq. (3) of this study and by Eq. (4) from Zhu et al. (2017). The former
307 performs very well as shown by an overwhelmingly large number of data points falling
308 along or overlapping the 1:1 line. By contrast, the latter overestimates DLR by 25 W⸱m-
11
309 2 (10%). This difference is not very likely due to different DLR measurements used to
310 produce Eq. (3) and (4) giving the following considerations. First, this systematic
311 overestimation is much larger than the expected uncertainty of DLR measurements (2.5%
312 or 4 W⸱m-2) (Stoffel, 2005). More important, comparison of cloudy DLR
313 parameterizations between this study and Zhu et al. (2017) showed good agreement
314 (not shown). Note that only 1-hour CG3 DLR observations are used for clear sky
315 discrimination in Zhu et al. (2017). This method was shown to be very likely
316 contaminated by the thin high cloud (Sutter et al., 2004). This certainly would produce
317 an overestimation of clear sky DLR parameterization since larger DLRs are associated
318 with potential residual clouds relative to real clear-sky DLRs.
319
320 4.2 Parameterization of cloudy-sky DLR
321 Parameterizations of cloudy-sky DLR (DLRcld) are based on estimated DLRclr
322 coupled with the effect of cloudiness or cloud emissivity, which depends primarily on
323 CF as well as other cloud parameters, like CBH and cloud type (Arking, 1990; Viúdez-
324 Mora et al., 2015). Four parameterizations (Table 4), which modifies the bulk
325 emissivity depending on CF, are assessed and locally calibrated in this section.
326 DLRclr is estimated according to Eq. (3). The fitted values of the coefficients (using
327 10-Fold Cross-Validation) of the four cloudy parameterizations are presented in Table
328 4. RMSE and R2 of original and locally fitted parameterizations over the TP are
329 presented in Fig. 4.
330 Relative to clear-sky conditions, cloudy parameterizations using the given
331 parameters have higher error RMSE (generally exceeding 35 W⸱m-2) except that
332 developed by Jacobs (1978) (RMSE of 18 W⸱m-2). R2 was generally smaller than 0.9.
333 RMSE values decrease significantly in Maykut and Church (1973) and Sugita and
334 Brutsaert (1993) as locally calibrated parameters are used. Relative smaller and almost
335 no RMSE improvements are found for the methods developed by Konzelmann (1994)
336 and Jacobs (1978).
337 Eq. (5) shows the best cloudy-sky parameterization over the TP by combining the
338 clear-sky parameterization of Dilley and O’Brien (1998) with the cloud modulation 12
339 correction scheme of Jacobs (1978). 1 푒 푇 6 46.50× 2 340 DLR = (1 + 0.23 × CF) × (59.38 + 113.70 × ( ) + 96.96 × ( 푇) ) (5) 푐푙푑 273.16 2.50 341 RMSE and R2 are ~18 W⸱m-2 and ~0.89 respectively. RMSE here is close to 15 W⸱m-2
342 obtained in different altitude areas in Swiss (Gubler et al., 2012) and slightly lower than
343 23 W⸱m-2 obtained in mountain area in Germany (Iziomon et al., 2003). Comparing to
344 previous studies over the TP (RMSE of 22 W⸱m-2 in Zhu et al., 2017), our cloudy model
345 produces better results.
346 In order to validate the newly developed DLR parameterizations, clear-sky and
347 cloudy-sky DLR parameterizations are validated against DLR measurements at Lhasa.
348 The results are shown in Fig. 5. Compared to the existed parameterizations, the Eq.(3)
349 and Eq.(5) produce the smallest bias (both less than 2 W·m-2) and RMSE (Eq.(3)’s is
350 less than 5 W·m-2 and Eq.(5)’s is less than 25 W·m-2). This independently demonstrates
351 the improved DLR parameterizations can be used in other stations over the TP.
352
353 4.3 Effect of CBH on DLR under Overcast Conditions
354 Since clouds behave approximately as a blackbody, the most relevant cloud
355 parameter (besides CF) to DLR under overcast skies (DLRovc) is CBH (Kato et al, 2011;
356 Viúdez-Mora et al., 2015): firstly, CBH defines the temperature of the lowest cloud
357 boundary, which through the Stefan-Boltzmann law drives the cloud emittance;
358 secondly, DLR emitted by the atmospheric layers above a cloud is totally absorbed by
359 the cloud itself (clouds are thick enough). Radiative transfer model simulation has
360 suggested that CBH under overcast conditions is an important modulator for DLR. The
361 cloud radiation effect (CRE), the difference between DLRobs and DLRclr, decreases with
362 increasing CBH at a rate of 4~12 W⸱m-2 that depends on climate profiles (Viúdez-Mora
363 et al., 2015). This indicates that overcast DLR parameterization would be improved if
364 CBH is considered.
365 A close relationship between CRE and CBH under overcast conditions over the TP
366 is presented in Fig 6. Compared to Viúdez-Mora (2015) results derived at Girona, Spain,
367 a mid-latitude site with low altitude, CRE over the TP is generally lower by 5~10 W⸱m-
13
368 2. This is likely because clouds over the TP with the same CBH as that at Girona have
369 relatively lower temperature, thereby producing lower radiative effect on DLR. CRE
370 generally decreases as CBH increases. The result agrees with the expectation since
371 CBH influence on DLR should decrease as CBH increases as a result of increasing
372 water vapor effects on DLR. According to Fig 6, CRE is about 70 W⸱m-2 for clouds <
373 1 km and decreases to ~40 W⸱m-2 for clouds at 3~4 km in TP. The decreasing rate of
374 CRE with CBH is estimated to be -9.8 W⸱m-2⸱km-1 over the TP that agrees with model
375 simulations (Viúdez-Mora et al., 2015).
376 Since CBH effect on overcast DLR is apparent, we introduced a modified
377 parameterization to consider CBH effect on DLR under overcast conditions. A linear
378 correlation is firstly established based on the measured CBH and the ratio of observed
obs cal 379 DLR (DLRovc) and calculated DLR by Eq.(5) (DLRovc) under overcast condition in Fig cal 380 6. Since we can see that DLRovc is equal to DLRclr times 1.23 (because CF is equal to
381 1 in Eq. 5), we derived a CBH corrected DLRovc parametrization as follows.
382 DLR표푣푐 = 1.23 × DLR푐푙푟 × (1.07–0.046 × CBH) (6)
383 Where CBH has unit of km. The bias and RMSE of Eq. (6) between measurements
384 and calculations is -2.15 W⸱m-2 and 19.79 W⸱m-2, respectively, which are significantly
385 lower than that of Eq. (5) (10.3 W⸱m-2 and 21.4 W⸱m-2) in overcast conditions. The
386 result indicates a remarkable improvement in the estimation of DLR under overcast
387 conditions by introducing CBH to the DLR parameterization; therefore, introduction of
388 such instruments as ceilometer to measure CBH is highly significant for studying
389 cloud’s impacts on DLR.
390
391 5 Discussion and conclusions
392 The parameterization of clear-sky DLR requires a well-defined distinction
393 between clear-sky and cloudy-sky situations that commonly depends on human cloud
394 observations 4~6 times each day. Human observation is subjective in nature and its low
395 temporal resolution cannot resolve dramatic high-resolution variation of clouds.
396 Furthermore, synoptic human cloud observations show the tendency to stronger weight
14
397 to the horizon that DLR is not highly sensitive (Marty and Philipona, 2004). Clear sky
398 discrimination based on hourly DSR or DLR measurements also tends to be very
399 suspect of residual clouds due to their low temporal resolution. Parameterization of
400 clear-sky DLR based on these two methods is hence very likely biased as a consequence
401 of selection of cloud contaminated clear-sky measurements. This would result in biased
402 estimation of cloud DLR effect since it is the difference between clear-sky and
403 measured all-sky DLRs (Dupont et al., 2008).
404 Using 1-minute DSR and DLR at 3 stations over the TP, DLR parameterizations
405 are evaluated and localized parameterizations have been developed based on a
406 comprehensive cloud-screening method. We test the fitted parameterizations based on
407 independent DLR measurements at Lhasa. Potential CBH effect on overcast DLR is
408 experimentally determined. Major conclusions are as follows.
409 Among 11 clear-sky DLR parameterizations tested in this study, two methods
410 using only atmospheric temperature largely deviate from other parameterizations. The
411 best method suitable for TP is the parameterization developed by Dilley and O’Brien
412 (1998). DLR estimation can be improved by localization of these parameterizations.
413 Locally calibrated parameterization can produce clear sky DLR with RMSE of 3.8
414 W⸱m-2.
415 Overcast DLR is highly sensitive to CBH. The parameterization can be
416 substantially improved by consideration of CBH effect. The bias between empirically
417 parameterized calculations and measurements decreases from 10.3 to 1.3 W⸱m-2.
418 The focus of this study is on daytime DLR parameterization over the TP since DSR
419 is used in the cloud-screening method. Given a significant role of DLR played in the
420 surface energy budget during nighttime, it is highly desirable to perform further study
421 on the nighttime DLR parametrization. These results are based on summer DLR
422 measurements, so the conclusions here need to be further tested in other seasons,
423 especially in winter when an increasing tendency of DLR has been observed (Rangwala
424 et al., 2009). Further investigations on these issues are expected to shed new light on
425 how and why DLR has changed over the TP. Our results clearly showed substantial
426 CBH effect on overcast DLR, which would be considered in future when ceilometer is 15
427 widely used to measure CBH.
428
429 Acknowledgements: This work was supported by the Strategic Priority Research
430 Program of Chinese Academy of Sciences (XDA17010101), the National Key R&D
431 Program of China (2017YFA0603504), the National Natural Science Foundation of
432 China (91537213, 91637107, and 41875183), the Special Fund for Meteorological
433 Research in the Public Interest (GYHY201106023), and the Science and Technological
434 Innovation Team Project of Chinese Academy of Meteorological Science (2013Z005)
435 respectively support the observations at AL, NQ and NC. We greatly appreciate Dr. Q.
436 He for providing the MPL Lidar measurement images and derived CBH data.
16
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569
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570
571 Table 1: Description of stations and measurements (magnitude and variability) at
572 three stations in the Tibetan Plateau
Site Altitude Period T (℃) e (hPa) DLR Data Points
(m ASL) (W⸱m-2)
NQ 4507 2011.7.20- 9.4±8 7.4±5 242.75±40 52980
2011.8.26
NC 2290 2014.6.7- 16.8±10 13.4±4 368.25±40 69609
2014.7.31
AL 4279 2016.5.27- 7.8±4 4.8±4 253.11±50 86596
2016.9.22
573 574
21
575 Table 2. 11 clear-sky DLR parameterizations and their specific conditions Reference Clear-Sky Parameterization Conditions
−0.067푒 4 Angstrom (1915) DLR푐푙푟 = {0.83 − 0.18 × 10 )}휎푇 Alt.: 1650~3500 T: 283.15~303.15 e: 4~1 4 Brunt (1932) DLR푐푙푟 = (0.52 + 0.065√푒)휎푇 Alt.: 6~3500 T: 269.15~303.15 e: 2.5~16 −13 6 Swinbank (1963) DLR푐푙푟 = 5.31 × 10 푇 Alt: 2 T: 281.15~302.15 e: 8~30
Idso and Jackson DLR푐푙푟 = (1 − 0.261 Alt.: 3, 331 (1969) ∙ exp(−0.000777 T: 228.15~318.15 × (273 − T)2))휎푇4 1 Brutsaert (1975) 푒 7 Alt.: 6~3500 DLR = 1.24 ( ) 휎푇4 푐푙푟 푇 T: 269.15~313.15 e: 2.5~-16 Satterlund (1979) 푇 Alt.: 594 DLR = 1.08 (1 − exp (−푒2016)) 휎푇4 푐푙푟 T: 236.15~309.15 e: 0~18hPa Idso (1981) Alt.: 331 DLR = (0.7 + 5.95 × 10−5 × 푒 푐푙푟 T: 258.15~278.15 1500 e: 2~6 × exp ( )) 휎푇4 푇
Konzelmann 1 Alt.: 340~3230 푒 8 (1994) DLR = (0.23 + 0.443 ( ) ) 휎푇4 T: 257.15~279.15 푐푙푟 푇 e: 1.5~5.5 Prata (1996) Not specified DLR =(1-(1+46.5푒) ×exp(-(1.2+3×46.5 푐푙푟 푇
푒)0.5)) 휎푇4 푇
Dilley and O’Brien 푇 6 Not specified DLR =59.38+113.7 ( ) + (1998) 푐푙푟 273.16
푒 96.96√46.5 /2.5 푇 Iziomon (2001) 11.5푒 Alt.: 1489 DLR = (1 − 0.43 exp (− )) 휎푇4 푐푙푟 푇 푇̅=277.55푒̅ =7.4
576 *Where Alt. is the altitude above sea level, and its unit is (m ASL), 푒 is screen-level water vapor
577 pressure in hPa and T represents surface temperature in K
578
579
22
580
581 Table 3. Locally fitted clear-sky DLR parameterizations in TP
Reference Locally fitted Clear-Sky Parameterization
−0.068푒 4 Angstrom(1915) DLR푐푙푟 = {0.8 − 0.19 × 10 )}휎푇
4 Brunt(1932) DLR푐푙푟 = (0.56 + 0.07√푒)휎푇
−13 6 Swinbank(1963) DLR푐푙푟 = 4.7 × 10 푇
2 4 Idso & Jackson(1969) DLR푐푙푟 = (1 − 0.36 ∙ exp(−0.00065 × (273 − 푇) ))휎푇
Brutsaert(1975) 푒 0.09 DLR = 1.03 ( ) 휎푇4 푐푙푟 푇 푇 Satterlun (1979) 4 DLR푐푙푟 = (1 − exp (−푒2016)) 휎푇
1500 Idso(1981) DLR = (0.63 + 7.5 × 10−5 × 푒 × exp ( )) 휎푇4 푐푙푟 푇
푒 0.13 Konzelmann(1994) DLR = (0.23 + 0.45 ( ) ) 휎푇4 푐푙푟 푇
푒 푒 Prata(1996) DLR =(1-(1+46.5 ) ×exp(-(1+3×46.5 )0.5)) 휎푇4 푐푙푟 푇 푇
푇 6 푒 Dilley and O’Brien(1998) DLR =-2.54+158.1 ( ) + 106.4√46.5 /2.5 푐푙푟 273.16 푇 14.52푒 Iziomon(2001) DLR = (1 − 0.38 exp (− )) 휎푇4 푐푙푟 푇 582
23
583 Table 4. 4 Ordinary and locally fitted cloudy-sky DLR parameterizations Ordinary Locally Fitted Reference DLRcld Parameterization Parameters Parameters a=0.7855 a=0.85 Maykut(1973) (a + b × CF푐)휎푇4 b=0.000312 b=0.01 c=2.75 c=3
Jacobs(1978) (1 + a × CF)DLR푐푙푟 a=0.26 a=0.23 a=0.0496 a=0.2 푏 Sugita(1993) (1 + a × CF ) DLR푐푙푟 b=2.45 b=1.3 a=4 a=3.5 푎 푎 4 Konzelmann(1994) (1 − CF )DLR푐푙푟 + b × CF 휎푇 b=0.95 b=1 584
24
585
25
586 587 Fig. 1. Time series of data sample on 2016.8.19 transited from clear‐sky to cloudy-sky: (a) 588 measured (black line) and calculated (dotted black line) downward shortwave radiation and its 21- 589 min standard deviation (grey line), (b) measured downward longwave radiation and 21-min standard 590 deviation and (c) MPL backscattering coefficient and the cloud base height.
26
591 592 Fig. 2. RMSE and R2 for the clear-sky DLR parameterizations using original (a) and 593 locally calibrated (b) coefficients. 594
27
595
596 597 Fig. 3. Scatter plots ofmeasured clear-sky DLR data from as a function of calculations 598 by the Eq.(3) this study (blue dots) and the Eq.(4) by Zhu et al. (2017) (red dots). The 599 dash black line is the 1:1 line. 600
28
601 2 602 Fig. 4. RMSE and R for the cloudy-sky DLR (DLRcld) parameterizations using the 603 original (blue) and locally calibrated (red) coefficient. 604
29
605 606 Fig. 5. BIAS and RMSE for the LDR parameterizations using (a) the published clear- 607 sky parameterizations and Eq.(3), and (b) cloudy-sky parameterizations and Eq.(5). 608 609
30
610
611 612 Fig. 6. Distributions of the ratio of observed DLR and calculated DLR by Eq.(5) under 613 overcast condition against measured cloud base height are represented by box plot (the 614 blue box indicates the 25th and 75th percentiles, the whiskers indicate 5th and 95th 615 percentiles, the red middle line is the median, the black plus sign is the mean). The 616 black triangle line is the fitting line.
31